MEK OF MATHEMATICS both Abel and Jacob! for 'wasting' their time on elliptic fune- •.. tions while there were still problems in heat-conduction to be: solved. 4 It is trae% Jacobi says, sthat M. Fourier had the opinion that the principal aim of mathematics was public utility and the explanation of natural phenomena; but a philosopher like Mm, should have known that the sole end of science is the honour of the human mind, and that under this title a question about numbers is worth as much as a question about the system of the world.* If Fourier could revisit the glimpses of the moon he might be disgusted at what has happened to the analysis he invented for 'public utility and the explanation of natural phenomena*. So far as mathematical physics is concerned Fourier analysis to- day is but a detail in the infinitely vaster theory of boundary- value problems, and it is in the purest of pure mathematics that the analysis which Fourier invented finds its interest and its justification. Whether 'the human mind' is honoured by these modern researches may be put up to the experts - provided the behaviourists have left anything of the human mind to be honoured.